The input arrays to this routine are designed to allow maximum flexibility in the supply of vector parameters by re-using elements of any arrays that are shorter than the total number of evaluations required. See Section 2.6 in the G01 Chapter Introduction for further information.

The solution did not converge in 600 iterations, see S14BAF for details. The probability returned should be a reasonable approximation to the solution.

11: IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to 0, -1​ or ​1. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value -1​ or ​1 is recommended. If the output of error messages is undesirable, then the value 1 is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is 0. When the value -1​ or ​1 is used it is essential to test the value of IFAIL on exit.

On exit: IFAIL=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry IFAIL=0 or -1, explanatory error messages are output on the current error message unit (as defined by X04AAF).

Errors or warnings detected by the routine:

IFAIL=1

On entry, at least one value of G, A, B or TAIL was invalid, or the solution did not converge.
Check IVALID for more information.

IFAIL=2

On entry, array size=value.
Constraint: LTAIL>0.

IFAIL=3

On entry, array size=value.
Constraint: LG>0.

IFAIL=4

On entry, array size=value.
Constraint: LA>0.

IFAIL=5

On entry, array size=value.
Constraint: LB>0.

IFAIL=-999

Dynamic memory allocation failed.

7 Accuracy

The result should have a relative accuracy of machine precision. There are rare occasions when the relative accuracy attained is somewhat less than machine precision but the error should not exceed more than 1 or 2 decimal places.

8 Further Comments

The time taken by G01SFF to calculate each probability varies slightly with the input parameters gi, αi and βi.

9 Example

This example reads in values from a number of gamma distributions and computes the associated lower tail probabilities.